Less than a week ago, Joel Embiid seemed out of the Celtics’ reach. The Kansas 7-footer was a top-three lock for Thursday’s NBA Draft, and likely the first pick overall, long gone before the Celtics’ No. 6 overall selection.

Then, almost out of the nowhere, the promising center had surgery last Friday for a stress fracture in his right foot, with two screws placed in the navicular bone. His projected recovery timetable: 4-6 months, at least.

Suddenly, Embiid’s stock started dropping, which created chaos at the top of the draft. Teams scrambled to gather medical information on him, while some speculated that Embiid could fall out of the top 10.

All that happened within days of the draft, giving teams a curveball that they won’t see often, if ever. “It’s a pretty unique situation,” said Celtics president of basketball operations Danny Ainge.

But on the eve of the draft, several league sources said that Embiid could fall to the Celtics at the sixth pick — and that the Celtics are expected to grab him if he’s there.

Though Embiid would miss summer league, training camp, and potentially part — if not all — of the 2014-15 season, he would give the Celtics a future “rim protector” that Ainge said the team needed when last season ended.

And though raw, Embiid’s burgeoning offensive game, which improved plenty during his freshman season at Kansas, would give them a valuable weapon down low.

One reason Embiid may fall to the Celtics, who also have the No. 17 pick in the first round, is because of how his medical information was doled out.

Embiid’s camp, and specifically his agent, Arn Tellem, controlled which teams had access to that information, and league sources said not every team with a top-10 pick received it. The Celtics, however, did.

There are multiple reasons why an agent would be selective with that information, but, essentially, teams that have it are more comfortable selecting that player, while teams that don’t are afraid to gamble without having such vital facts.

The Celtics’ medical staff has advised the team to pass on specific players before, and the team also has drafted players who had medical concerns entering the draft, specifically Avery Bradley in 2010 and Jared Sullinger in 2012.

Embiid might be a little more tricky, not only because of his recent foot surgery but because he also suffered a stress fracture in his back earlier this year. Both back and foot injuries historically have been nagging issues for centers.

Embiid has said that his back has healed, and a league source said that’s true, though the source added that a team would be wise to have Embiid engage in back-specific training to further strengthen it.

The foot issue is more of a question mark because centers have a bad history with navicular bone fractures; they notably ended the careers of Yao Ming and Bill Walton.

But Dr. Kenneth Hunt, an assistant professor of orthopedic surgery at the Stanford University Medical Center, pointed out that both Ming and Walton had such fractures late in their career — and that Embiid is just 20 years old.

“The fact that [Embiid is] young, his body has a much better potential to heal than if this were to happen in his mid-to-late 30s towards the end of an NBA career,” Hunt said. “He has a higher chance of healing completely and also more rapidly given his young age.”

The navicular bone is at the top of the foot and is crucial for running and jumping, but centers typically fracture it because of the amount of weight and pressure they put on it.

Dr. Dennis Nutini, Medical Director of the Spaulding Outpatient Center in Brighton and a sports medicine specialist, was asked what advice he’d give an NBA GM who was considering drafting Embiid.

“There’s always chance, but without any other risk factors, without any reason to believe that he would have poor bone healing – like bone deficiencies or nutritional factors or things that could affect that – then he should be just fine,” Nutini said.

“The chances are well in his favor to do well after the surgery in the long term. Is [the recovery] four months? Is it six months? Is it eight months? That might take time. I would err on [the side of] not rushing him back. I think you run into a bigger issue if you rush him back sooner than if he’s ready, than if the pain has gone away.

“After the surgery, you want to make sure it’s not really tender in that area. You kind of want to baby it and then get him back with a gradual rehab program. I think if everything goes smoothly with that and he’s not rushing back, then things should go well.”

Hunt, who is also a clinical consultant for the Golden State Warriors and the San Francisco 49ers, agreed.

“The fact that it was identified early and treated early all portend a positive prognostication for him and a high chance that he’ll be able to compete in a high level in the NBA,” Hunt said. “I don’t think this injury will limit him long term.”

That’s what the Celtics will be hoping for — if, in fact, Embiid falls in their lap.